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Math Help - prove H is an abelian group

  1. #1
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    prove H is an abelian group

    g=I for all h is an element of H.
    a)Prove: H is an abelian group
    b)Prove: Suppose |H|<∞. Let {h₁,h₂,…..hn} be minimal set of generators for H. then
    Last edited by apple2009; November 8th 2009 at 06:13 PM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by apple2009 View Post
    g=I for all h is an element of H.
    a)Prove: H is an abelian group
    b)Prove: Suppose |H|<∞. Let {h₁,h₂,…..hn} be minimal set of generators for H. The |H|=2^n
    Problem: Suppose G is a group such that g^2=e_G\quad\forall g\in G. Prove that G is abelian.

    Proof (1): Note that g^2=e\implies g=g^{-1}. Therefore \left(ab\right)=\left(ab\right)^{-1}=b^{-1}a^{-1}=ba.

    Proof (2): Using the above we can see that ab=a\left(e_G\right)b=a(ab)^2b=(aa)ba(bb)=a^2bab^2  =ba

    Part b doesn't make sense. Is there a typo?
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by apple2009 View Post
    g=I for all h is an element of H.
    a)Prove: H is an abelian group
    b)Prove: Suppose |H|<∞. Let {h₁,h₂,..hn} be minimal set of generators for H. The |H|=2^n
    I think it should be "then \left|H\right|=2^n. If so, I think you ought to be able to make a contrived answer from the way the question is posed. What is significant looking about that expression?
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